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2005-11+Test2S

# 2005-11+Test2S - ECMB11H3 Quantitative Methods in Economics...

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1 ECMB11H3 Quantitative Methods in Economics I Section L30, Fall 2005 Division of Management and Economics University of Toronto at Scarborough Dr. Yu Test 2 Date: Wednesday, November 16, 2005 Time allowed: Two (2) hours Aids allowed: Calculator and one aid sheet (two 8.5"x11" pages) Notes: This test consists of 20 questions in 9 pages including this cover page. It is the student’s responsibility to hand in a complete test. Any missing page will get a zero mark. Statistical tables (Binomial, Poisson and Standard Normal) are provided separately. Show your work in part 2. No marks will be given if you do not show your work. This test is worth 30% of your course grade. Print Last Name: Solution Given Name: Student Number: Do not write on the space below, for markers only. Page Question Total Mark 2-5 1-20 60 6 21 10 7 22 10 8 23 10 9 24 10 Total 100

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2 Part 1 Multiple Choice. 3 marks for each question. Select the BEST answer. No part marks. 1. Let X be a random variable with probability density function below. () = elsewhere k k x f , 0 2 2 , The probability () 1 < X P is equal to (a) 0.15 (b) 0.25 (c) 0.5 (d) 0.65 (e) 0.75 2. Forty percent of business travelers carry a laptop. In a random sample of 15 business travelers, the probability that 12 or more carry laptops is closest to (a) 0.0019 (b) 0.0025 (c) 0.0031 (d) 0.0037 (e) 0.0042 3. A machining operation produces bearings with diameters that are normally distributed with mean 3 centimeters and a standard deviation 0.5 centimeters. Specifications require the bearing diameters to lie in the interval 8 . 0 3 ± centimeters. Those outside the interval are considered scrap and must be re-machined. What percent of the total production will be scrap? (a) 0.0548 (b) 0.1096 (c) 0.2131 (d) 0.3052 (e) 0.4452 Questions 4-5, use the following information . Customers arrive at a bookstore at a Poisson rate of six per hour. Given that the bookstore opens at 9:00 am. 4. What is the probability that more than 2 customers arrive by 10:00 am? (a) 0.062 (b) 0.1512 (c) 0.7741 (d) 0.8488 (e) 0.938 5. What is the probability that more than 2 customers arrive in each hour for the next 3 hours? (a) 0.062 (b) 0.1512 (c) 0.7741 (d) 0.8253 (e) 0.938
3 Questions 6-7, use the following information . Suppose that a student is considering one of the two possible summer jobs to take. If the student takes a summer course, then a part-time job at a hotel will produce earnings (rounded to the nearest \$1000) with the following probability distribution. Earning \$1000 \$2000 \$3000 \$4000 Probability 0.3 0.4 0.2 0.1 If the student does not take a summer course, then a job as a waiter will produce earnings (rounded to the nearest \$1000) with the following probability distribution. Earning

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2005-11+Test2S - ECMB11H3 Quantitative Methods in Economics...

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